Question

A basketball player makes 80% of his free throw.?

A- Attempt 13 shoots determine probability they make 10 .
B-Attempt 6 free throws what is probability they miss not more than 2 ?

Answer 1

this is a simple usage of binomial probability formula: http://www.allianthawk.org/images/stats%20binomial%20probability%20formula.gif

A -
player shoots 13 times, chance of hitting 80% or 0.8 and the chance of missing 20% or 0.2

chance that a player will hit the basket exactly 10 times out of 13 tries is equal to:

p(X = 10) = (13 nCr 10) * (0.8)^10 * (0.2)^3 = 0.2456 or 24.56%

EXPLANATION OF NUMBERS IN BINOMIAL FORMULA: (13 nCr 10) means we are picking out which 10 throws out of 13 he'll score (instead of picking out throws he'll score, we could have picked throws that he'll miss, writing down (13 nCr 3), it is the same thing), (0.8)^10 is probability of hitting 10 throws and (0.2)^3 is probability of missing 3 throws

B -
"probability they miss not more than 2" means player will miss either 0, 1 or 2 throws, no more than that; we use the same formula like in the A part of the assignment

p(X <= 2) = p(X=0) + p(X=1) + p(X=2) = (0.8)^6 + (6 nCr 1) * (0.8)^5 * (0.2)^1 + (6 nCr 2) * (0.8)^4 * (0.2)^2 = 0.262 + 0.393 + 0.246 = 0.901 or 90.1%

Answer 2

Thank you very much